As with CronoDAS's suggestion of a pseudorandom generator, this can easily yield variables possessing a strong causal connection but no correlation.

Correlations -- product-moment or any other statistical calculation -- are machines to detect relationships between variables that are obscured by passive fog. Random generators and cryptosystems are machines to defeat detection even by an adversary. It is not a surprise that crypto beats correlation.

More surprising is the existence of systems as simple as B = dA/dt which also defeat correlation. The scatter-plot looks like pure fog, yet there are no extraneous noise sources and no adversarial concealment. The relationship between the variables is simply invisible to the statistical tools used in causal analysis.